Technical Mathematics / Edition 6

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This textbook has been in constant use since 1980, and this editionrepresents the first major revision of this text since the secondedition. It was time to select, make hard choices of material,polish, refine, and fill in where needed. Much has been rewrittento be even cleaner and clearer, new features have been introduced,and some peripheral topics have been removed.

The authors continue to provide real-world, technicalapplications that promote intuitive reader learning. Numerousfully worked examples and boxed and numbered formulas give studentsthe essential practice they need to learn mathematics. Computerprojects are given when appropriate, including BASIC, spreadsheets,computer algebra systems, and computer-assisted drafting. Thegraphing calculator has been fully integrated and calculatorscreens are given to introduce computations. Everything thetechnical student may need is included, with the emphasis always onclarity and practical applications.

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Product Details

  • ISBN-13: 9780470534922
  • Publisher: Wiley
  • Publication date: 3/22/2011
  • Edition description: New Edition
  • Edition number: 6
  • Pages: 832
  • Product dimensions: 8.80 (w) x 10.90 (h) x 1.30 (d)

Meet the Author

Paul Calter is Professor Emeritus of Mathematics at Vermont Technical College and Visiting Scholar at Dartmouth College. A graduate of The Cooper Union, New York, he received his M.S. from Columbia University and a MFA from Norwich University. Professor Calter has taught technical mathematics for over twenty-five years. He is a member of the American Mathematical Association of Two  Year Colleges, the Mathematical Association of America, the National Council of Teachers of Mathematics, the College Art Association, and the Author's Guild.

Calter is involved in the Mathematics Across the Curriculum movement, and has developed and taught a course called Geometry in Art and Architecture at Dartmouth College under an NSF grant.

Professor Calter is the author of several other mathematics textbooks, among which are the Schaum's Outline of Technical Mathematics, Problem Solving with Computers, Practical Math Handbook for the Building Trades, Practical Math for Electricity and Electronics, Mathematics for Computer Technology, Introductory Algebra and Trigonometry, Technical Calculus, and Squaring the Circle: Geometry in Art and Architecture.

Michael Calter is Associate Professor at Wesleyan University. He received his B.S. from the University of Vermont. After receiving his Ph.D. from Harvard University, he completed a post-doctoral fellowship at the University of California at Irvine. Michael has been working on his father's mathematics texts since 1983, when he completed a set of programs to accompany Technical Mathematics with Calculus. Since that time, he has become progressively more involved with his father's writing endeavors, culminating with becoming co-author on the second edition of Technical Calculus and the fourth edition of Technical Mathematics with Calculus. Michael also enjoys the applications of mathematical techniques to chemical and physical problems as part of his academic research. Michael is a member of the American Mathematical Association of Two Year Colleges, the American Association for the Advancement of Science, and the American Chemical Society.

Michael and Paul enjoy hiking and camping trips together. These have included an expedition up Mt. Washington in January, a hike across Vermont, a walk across England on Hadrian's Wall, and many sketching trips into the mountains.

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Table of Contents

1 Review of Numerical Computation 1

1–1 The Real Numbers 2

1–2 Addition and Subtraction 9

1–3 Multiplication 15

1–4 Division 19

1–5 Powers and Roots 23

1–6 Combined Operations 29

1–7 Scientific Notation and Engineering Notation32

1–8 Units of Measurement 41

1–9 Percentage 51

Chapter 1 Review Problems 59

2 Introduction to Algebra 62

2–1 Algebraic Expressions 63

2–2 Adding and Subtracting Polynomials 67

2–3 Laws of Exponents 72

2–4 Multiplying a Monomial by a Monomial 80

2–5 Multiplying a Monomial and a Multinomial 83

2–6 Multiplying a Binomial by a Binomial 86

2–7 Multiplying a Multinomial by a Multinomial88

2–8 Raising a Multinomial to a Power 90

2–9 Dividing a Monomial by a Monomial 92

2–10 Dividing a Polynomial by a Monomial 95

2–11 Dividing a Polynomial by a Polynomial 98

Chapter 2 Review Problems 101

3 Simple Equations and Word Problems 103

3–1 Solving a Simple Equation 104

3–2 Solving Word Problems 113

3–3 Uniform Motion Applications 118

3–4 Money Problems 121

3–5 Applications Involving Mixtures 123

3–6 Statics Applications 127

3–7 Applications to Work, Fluid Flow, and EnergyFlow 129

Chapter 3 Review Problems 133

4 Functions 136

4–1 Functions and Relations 137

4–2 More on Functions 144

Chapter 4 Review Problems 154

5 Graphs 156

5–1 Rectangular Coordinates 157

5–2 Graphing an Equation 161

5–3 Graphing a Function by Calculator 164

5–4 The Straight Line 167

5–5 Solving an Equation Graphically 172

Chapter 5 Review Problems 173

6 Geometry 175

6–1 Straight Lines and Angles 176

6–2 Triangles 180

6–3 Quadrilaterals 187

6–4 The Circle 190

6–5 Polyhedra 196

6–6 Cylinder, Cone, and Sphere 201

Chapter 6 Review Problems 205

7 Right Triangles and Vectors 207

7–1 The Trigonometric Functions 208

7–2 Solution of Right Triangles 212

7–3 Applications of the Right Triangle 216

7–4 Angles in Standard Position 221

7–5 Introduction to Vectors 222

7–6 Applications of Vectors 226

Chapter 7 Review Problems 229

8 Oblique Triangles and Vectors 231

8–1 Trigonometric Functions of Any Angle 232

8–2 Finding the Angle When the TrigonometricFunction Is Known 236

8–3 Law of Sines 240

8–4 Law of Cosines 246

8–5 Applications 251

8–6 Non-Perpendicular Vectors 255

Chapter 8 Review Problems 260

9 Systems of Linear Equations 263

9–1 Systems of Two Linear Equations 264

9–2 Applications 270

9–3 Other Systems of Equations 279

9–4 Systems of Three Equations 284

Chapter 9 Review Problems 290

10 Matrices and Determinants 292

10–1 Introduction to Matrices 293

10–2 Solving Systems of Equations by the UnitMatrix Method 297

10–3 Second-Order Determinants 302

10–4 Higher-Order Determinants 308

Chapter 10 Review Problems 316

11 Factoring and Fractions 319

11–1 Common Factors 320

11–2 Difference of Two Squares 323

11–3 Factoring Trinomials 326

11–4 Other Factorable Expressions 333

11–5 Simplifying Fractions 335

11–6 Multiplying and Dividing Fractions 340

11–7 Adding and Subtracting Fractions 344

11–8 Complex Fractions 349

11–9 Fractional Equations 352

11–10 Literal Equations and Formulas 355

Chapter 11 Review Problems 360

12 Quadratic Equations 363

12–1 Solving a Quadratic Equation Graphically andby Calculator 364

12–2 Solving a Quadratic by Formula 368

12–3 Applications 372

Chapter 12 Review Problems 377

13 Exponents and Radicals 379

13–1 Integral Exponents 380

13–2 Simplification of Radicals 385

13–3 Operations with Radicals 392

13–4 Radical Equations 398

Chapter 13 Review Problems 403

14 Radian Measure, Arc Length, and Rotation405

14–1 Radian Measure 406

14–2 Arc Length 413

14–3 Uniform Circular Motion 416

Chapter 14 Review Problems 420

15 Trigonometric, Parametric, and Polar Graphs422

15–1 Graphing the Sine Wave by Calculator 423

15–2 Manual Graphing of the Sine Wave 430

15–3 The Sine Wave as a Function of Time 435

15–4 Graphs of the Other Trigonometric Functions441

15–5 Graphing a Parametric Equation 448

15–6 Graphing in Polar Coordinates 452

Chapter 15 Review Problems 459

16 Trigonometric Identities and Equations 461

16–1 Fundamental Identities 462

16–2 Sum or Difference of Two Angles 469

16–3 Functions of Double Angles and Half-Angles474

16–4 Evaluating a Trigonometric Expression 481

16–5 Solving a Trigonometric Equation 484

Chapter 16 Review Problems 489

17 Ratio, Proportion, and Variation 491

17–1 Ratio and Proportion 492

17–2 Similar Figures 497

17–3 Direct Variation 501

17–4 The Power Function 505

17–5 Inverse Variation 509

17–6 Functions of More Than One Variable 513

Chapter 17 Review Problems 518

18 Exponential and Logarithmic Functions 521

18–1 The Exponential Function 522

18–2 Logarithms 532

18–3 Properties of Logarithms 539

18–4 Solving an Exponential Equation 547

18–5 Solving a Logarithmic Equation 554

Chapter 18 Review Problems 560

19 Complex Numbers 562

19–1 Complex Numbers in Rectangular Form 563

19–2 Complex Numbers in Polar Form 568

19–3 Complex Numbers on the Calculator 572

19–4 Vector Operations Using Complex Numbers575

19–5 Alternating Current Applications 578

Chapter 19 Review Problems 584

20 Sequences, Series, and the Binomial Theorem586

20–1 Sequences and Series 587

20–2 Arithmetic and Harmonic Progressions 593

20–3 Geometric Progressions 600

20–4 Infinite Geometric Progressions 604

20–5 The Binomial Theorem 607

Chapter 20 Review Problems 614

21 Introduction to Statistics and Probability617

21–1 Definitions and Terminology 618

21–2 Frequency Distributions 622

21–3 Numerical Description of Data 628

21–4 Introduction to Probability 638

21–5 The Normal Curve 648

21–6 Standard Errors 654

21–7 Process Control 661

21–8 Regression 669

Chapter 21 Review Problems 674

22 Analytic Geometry 679

22–1 The Straight Line 680

22–2 Equation of a Straight Line 687

22–3 The Circle 694

22–4 The Parabola 702

22–5 The Ellipse 713

22–6 The Hyperbola 725

Chapter 22 Review Problems 733


A Summary of Facts and Formulas A-0

B Conversion Factors A-0

C Table of Integrals A-0


Applications Index I-0

Index to Writing Questions I-0

Index to Projects I-0

General Index I-0

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